{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:50:07Z","timestamp":1759063807014},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2011,6]]},"abstract":"<jats:p> A maximum stable set in a graph G is a stable set of maximum cardinality. S is a local maximum stable set of G, and we write S \u2208 \u03a8(G), if S is a maximum stable set of the subgraph induced by S \u222a N(S), where N(S) is the neighborhood of S. Nemhauser and Trotter Jr. [Vertex packings: structural properties and algorithms, Math. Program.8 (1975) 232\u2013248], proved that any S \u2208 \u03a8(G) is a subset of a maximum stable set of G. In [Levit and Mandrescu, A new greedoid: the family of local maximum stable sets of a forest, Discrete Appl. Math.124 (2002) 91\u2013101] we have shown that the family \u03a8(T) of a forest T forms a greedoid on its vertex set. The cases where G is bipartite, triangle-free, well-covered, while \u03a8(G) is a greedoid, were analyzed in [Levit and Mandrescu, Local maximum stable sets in bipartite graphs with uniquely restricted maximum matchings, Discrete Appl. Math.132 (2004) 163\u2013174], [Levit and Mandrescu, Triangle-free graphs with uniquely restricted maximum matchings and their corresponding greedoids, Discrete Appl. Math.155 (2007) 2414\u20132425], [Levit and Mandrescu, Well-covered graphs and greedoids, Proc. 14th Computing: The Australasian Theory Symp. (CATS2008), Wollongong, NSW, Conferences in Research and Practice in Information Technology, Vol. 77 (2008) 89\u201394], respectively. In this paper we demonstrate that if G is a very well-covered graph of girth \u22654, then the family \u03a8(G) is a greedoid if and only if G has a unique perfect matching. <\/jats:p>","DOI":"10.1142\/s1793830911001115","type":"journal-article","created":{"date-parts":[[2011,7,13]],"date-time":"2011-07-13T13:20:39Z","timestamp":1310563239000},"page":"245-252","source":"Crossref","is-referenced-by-count":5,"title":["VERY WELL-COVERED GRAPHS OF GIRTH AT LEAST FOUR AND LOCAL MAXIMUM STABLE SET GREEDOIDS"],"prefix":"10.1142","volume":"03","author":[{"given":"VADIM E.","family":"LEVIT","sequence":"first","affiliation":[{"name":"Ariel University Center of Samaria, Israel"}]},{"given":"EUGEN","family":"MANDRESCU","sequence":"additional","affiliation":[{"name":"Holon Institute of Technology, Israel"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511662041.009"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70387-X"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(94)90253-4"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(79)90066-9"},{"key":"rf5","first-page":"16","volume":"38","author":"Egervary E.","journal-title":"Mat. Lapok"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(82)90215-1"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.2001.1167"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-001-0004-z"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-58191-5"},{"key":"rf10","first-page":"116","volume":"38","author":"K\u00f6nig D.","journal-title":"Mat. Lapok"},{"key":"rf11","first-page":"209","volume":"130","author":"Levit V. E.","journal-title":"Congr. Numer."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(01)00332-8"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(02)00528-9"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(03)00398-6"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2007.05.039"},{"key":"rf16","first-page":"97","volume":"186","author":"Levit V. E.","journal-title":"Congr. Numer."},{"key":"rf18","first-page":"183","volume":"197","author":"Levit V. E.","journal-title":"Congr. Numer."},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580444"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(70)80011-4"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230220304"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(79)90085-6"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830911001115","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T16:13:15Z","timestamp":1565194395000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830911001115"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6]]},"references-count":21,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2011,6]]}},"alternative-id":["10.1142\/S1793830911001115"],"URL":"https:\/\/doi.org\/10.1142\/s1793830911001115","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,6]]}}}